The Covid-19 is a highly contagious and virulent disease caused by the Severe Acute Respiratory Syndrome - Corona Virus - 2 (SARS-CoV-2). Over 175 million cases and 3.8 million deaths were reported worldwide as of June 2021. Covid-19 disease induces lung changes observed in lung Computerized Tomography (CT) predominantly as ground-glass opacification (GGO) with occasional consolidation in the peripheries. It was revealed in some literature that 88% of Covid-19 positive patients' CT scans showed GGO and 32% showed consolidation. Moreover, it was reported that the percentage of the lung showing GGO, and consolidation is tied to disease severity. Thus, segmentation of ground-glass opacities and consolidations in CT images will help to quantify disease severity and assist physicians in disease triage, management, and prognosis. In this paper, we propose CoviSegNet, an enhanced U-Net model to segment these ground-glass opacities and consolidations. The performance of CoviSegNet was evaluated on three public CT datasets. The experimental results show that the proposed CoviSegNet is highly promising.